3tan`theta` + cot`theta` =5cosec`theta`

If 0^@ le theta le 90^@ , find the value of theta satisfying 3 tan theta + cot theta =5 cosec theta

Prove that : (tan theta)/(1 -cot theta) + (cot theta)/(1- tan theta) = 1 + cos theta cosec theta

Consider the following statements : 1. If ("cos"theta)/(1-"sin"theta)+("cos"theta)/(1+"sin"theta)=4 , where 0ltthetalt90^(@) , then theta=60^(@) . 2. If 3"tan"theta+"cot"theta=5"cosec"theta , where 0ltthetalt90^(@) , then theta=60^(@) . Which of the statements given above is/are correct ?

Prove that : (tan theta)/(1 -cot theta) + (cot theta)/(1- tan theta) = 1 + sec theta cosec theta

Eliminate theta, if x = 3 cosec theta + 4 cot theta, y = 4 cosec theta - 3 cot theta .

Prove that cot^(2)""(theta)/(2) - tan^(2) ""(theta)/(2) = 4 cot theta cosec theta .

Prove that (tan theta)/(1-cot theta)+(cot theta)/(1-tan theta) = (sec theta cosec theta +1)

Prove each of the following identities : (i) ("cosec"theta + cot theta )/("cosec"theta - cot theta ) = ("cosec" theta + cot theta)^(2) = 1+2cot^(2) theta + 2"cosec" theta cot theta (ii) (sec theta + tan theta ) /( sec theta - tan theta) =(sec theta + tan theta )^(2) = 1+ 2tan^(2) theta + 2 sec theta tan theta